I recently published a paper on designing surfaces that are stable under gravity: www.cs.columbia.edu/cg/pdfs/188-selfsupporting.pdf

I would now like to take an example of a surface designed on the computer, and realize it in real life. In particular, I would like to print the surface on the right of Figure 1.

To do this I would need to print two parts:
a) A single (hollow) volume, representing the space between the surface in Figure 1 and the floor. This piece will be used as a scaffolding for constructing the surface.
b) All of the faces of the surface. As you can see, there are about 100 pieces. I will then assemble the pieces into the structure shown in Figure 1.

Can this be done using shapeways? Can I upload the pieces as a single .obj file containing disconnected volumes? Is there a way of easily labeling each piece (to ease putting the surface together afterwards)?